Genetic variation is known to influence the amount of mRNA produced by a gene. Because molecular machines control mRNA levels of multiple genes, we expect genetic variation in components of these machines would influence multiple genes in a similar fashion. We show that this assumption is correct by using correlation of mRNA levels measured from multiple tissues in mouse strain panels to detect shared genetic influences. These correlating groups of genes (CGGs) have collective properties that on average account for 52-79% of the variability of their constituent genes and can contain genes that encode functionally related proteins. We show that the genetic influences are essentially tissue-specific and, consequently, the same genetic variations in one animal may upregulate a CGG in one tissue but downregulate the CGG in a second tissue. We further show similarly paradoxical behaviour of CGGs within the same tissues of different individuals. Thus, this class of genetic variation can result in complex inter- and intraindividual differences. This will create substantial challenges in humans, where multiple tissues are not readily available.